Subgroups — C₂²×C₃×C₈×C₁₆² #72201876

Order 24576.

158492 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈²×C₁₆	C₂	1	3	yes	maximal
2	C₂²×C₃×C₄×C₁₆²	C₂	1	4	yes	maximal
3	C₂×C₃×C₈×C₁₆²	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₈×C₁₆²	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₈³	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄×C₈×C₁₆	C₄	1	12	yes	—
7	C₂²×C₃×C₄×C₈×C₁₆	C₂²	1	6	yes	—
8	C₂×C₃×C₈²×C₁₆	C₄	1	36	yes	—
9	C₂×C₃×C₈²×C₁₆	C₂²	1	36	yes	—
10	C₂³×C₃×C₁₆²	C₄	1	16	yes	—
11	C₂×C₃×C₄×C₁₆²	C₄	1	48	yes	—
12	C₂×C₃×C₄×C₁₆²	C₂²	1	48	yes	—
13	C₃×C₈×C₁₆²	C₂²	1	64	yes	direct product factor
14	C₂²×C₈²×C₁₆	C₂×C₃	1	3	yes	—
15	C₂²×C₄×C₁₆²	C₂×C₃	1	4	yes	—
16	C₂×C₈×C₁₆²	C₂×C₃	1	24	yes	direct product factor
17	C₂²×C₃×C₄×C₈²	C₂×C₄	1	6	yes	—
18	C₂²×C₃×C₄×C₈²	C₂³	1	1	yes	characteristic
19	C₂×C₃×C₈³	C₂×C₄	1	18	yes	—
20	C₂×C₃×C₈³	C₂³	1	6	yes	—
21	C₂²×C₃×C₄²×C₁₆	C₂×C₄	1	12	yes	—
22	C₂×C₃×C₄×C₈×C₁₆	C₈	1	144	yes	—
23	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	36	yes	—
24	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	72	yes	—
25	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	144	yes	—
26	C₂×C₃×C₄×C₈×C₁₆	C₂³	1	36	yes	—
27	C₂³×C₃×C₈×C₁₆	C₈	1	48	yes	—
28	C₂³×C₃×C₈×C₁₆	C₂×C₄	1	24	yes	—
29	C₃×C₈²×C₁₆	C₂×C₄	1	144	yes	—
30	C₃×C₈²×C₁₆	C₂³	1	48	yes	—
31	C₂²×C₃×C₁₆²	C₈	1	256	yes	direct product factor
32	C₂²×C₃×C₁₆²	C₂×C₄	1	192	yes	—
33	C₃×C₄×C₁₆²	C₂×C₄	1	192	yes	—
34	C₃×C₄×C₁₆²	C₂³	1	64	yes	—
35	C₂²×C₈³	C₂²×C₃	1	1	yes	characteristic
36	C₂²×C₄×C₈×C₁₆	C₃×C₄	1	12	yes	—
37	C₂²×C₄×C₈×C₁₆	C₂²×C₃	1	6	yes	—
38	C₂×C₈²×C₁₆	C₃×C₄	1	36	yes	—
39	C₂×C₈²×C₁₆	C₂²×C₃	1	36	yes	—
40	C₂×C₄×C₁₆²	C₃×C₄	1	48	yes	—
41	C₂×C₄×C₁₆²	C₂²×C₃	1	48	yes	—
42	C₂³×C₁₆²	C₃×C₄	1	16	yes	—
43	C₈×C₁₆²	C₂²×C₃	1	64	yes	direct product factor
44	C₂²×C₃×C₄²×C₈	C₄²	1	4	yes	—
45	C₂²×C₃×C₄²×C₈	C₂²×C₄	1	3	yes	—
46	C₂³×C₃×C₈²	C₂×C₈	1	24	yes	—
47	C₂³×C₃×C₈²	C₂²×C₄	1	4	yes	—
48	C₂×C₃×C₄×C₈²	C₄²	1	36	yes	—
49	C₂×C₃×C₄×C₈²	C₂×C₈	1	72	yes	—
50	C₂×C₃×C₄×C₈²	C₂²×C₄	1	9	yes	—
51	C₂×C₃×C₄×C₈²	C₂²×C₄	1	12	yes	—
52	C₂×C₃×C₄×C₈²	C₂²×C₄	1	36	yes	—
53	C₂×C₃×C₄×C₈²	C₂⁴	1	3	yes	—
54	C₃×C₈³	C₄²	1	24	yes	—
55	C₃×C₈³	C₂²×C₄	1	36	yes	—
56	C₃×C₈³	C₂⁴	1	4	yes	—
57	C₂³×C₃×C₄×C₁₆	C₄²	1	24	yes	—
58	C₂³×C₃×C₄×C₁₆	C₂×C₈	1	48	yes	—
59	C₂×C₃×C₄²×C₁₆	C₄²	1	72	yes	—
60	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	144	yes	—
61	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	72	yes	—
62	C₂²×C₃×C₈×C₁₆	C₁₆	1	768	yes	direct product factor
63	C₂²×C₃×C₈×C₁₆	C₄²	1	144	yes	—
64	C₂²×C₃×C₈×C₁₆	C₂×C₈	1	576	yes	—
65	C₂²×C₃×C₈×C₁₆	C₂×C₈	1	384	yes	—
66	C₂²×C₃×C₈×C₁₆	C₂²×C₄	1	144	yes	—
67	C₃×C₄×C₈×C₁₆	C₄²	1	144	yes	—
68	C₃×C₄×C₈×C₁₆	C₂×C₈	1	576	yes	—
69	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	72	yes	—
70	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	144	yes	—
71	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	192	yes	—
72	C₃×C₄×C₈×C₁₆	C₂⁴	1	24	yes	—
73	C₂×C₃×C₁₆²	C₂×C₈	1	1536	yes	direct product factor
74	C₂×C₃×C₁₆²	C₂²×C₄	1	256	yes	—
75	C₂²×C₄×C₈²	C₂×C₃×C₄	1	6	yes	—
76	C₂²×C₄×C₈²	C₂³×C₃	1	1	yes	characteristic
77	C₂×C₈³	C₂×C₃×C₄	1	18	yes	—
78	C₂×C₈³	C₂³×C₃	1	6	yes	—
79	C₂²×C₄²×C₁₆	C₂×C₃×C₄	1	12	yes	—
80	C₂³×C₈×C₁₆	C₃×C₈	1	48	yes	—
81	C₂³×C₈×C₁₆	C₂×C₃×C₄	1	24	yes	—
82	C₂×C₄×C₈×C₁₆	C₃×C₈	1	144	yes	—
83	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	36	yes	—
84	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	72	yes	—
85	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	144	yes	—
86	C₂×C₄×C₈×C₁₆	C₂³×C₃	1	36	yes	—
87	C₈²×C₁₆	C₂×C₃×C₄	1	144	yes	—
88	C₈²×C₁₆	C₂³×C₃	1	48	yes	—
89	C₂²×C₁₆²	C₃×C₈	1	256	yes	direct product factor
90	C₂²×C₁₆²	C₂×C₃×C₄	1	192	yes	—
91	C₄×C₁₆²	C₂×C₃×C₄	1	192	yes	—
92	C₄×C₁₆²	C₂³×C₃	1	64	yes	—
93	C₂⁴×C₃×C₁₆	C₄×C₈	1	48	yes	—
94	C₂³×C₃×C₄×C₈	C₄×C₈	1	24	yes	—
95	C₂³×C₃×C₄×C₈	C₂×C₄²	1	6	yes	—
96	C₂³×C₃×C₄×C₈	C₂²×C₈	1	12	yes	—
97	C₂²×C₃×C₄³	C₂×C₄²	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	288	yes	—
99	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	384	yes	—
100	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	144	yes	—
101	C₂²×C₃×C₄×C₁₆	C₂×C₁₆	1	768	yes	—
102	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	144	yes	—
103	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	288	yes	—
104	C₂×C₃×C₄²×C₈	C₄×C₈	1	72	yes	—
105	C₂×C₃×C₄²×C₈	C₂×C₄²	1	9	yes	—
106	C₂×C₃×C₄²×C₈	C₂×C₄²	1	18	yes	—
107	C₂×C₃×C₄²×C₈	C₂×C₄²	1	24	yes	—
108	C₂×C₃×C₄²×C₈	C₂²×C₈	1	36	yes	—
109	C₂×C₃×C₄²×C₈	C₂³×C₄	1	9	yes	—
110	C₂²×C₃×C₈²	C₄×C₈	1	144	yes	—
111	C₂²×C₃×C₈²	C₂×C₁₆	1	384	yes	—
112	C₂²×C₃×C₈²	C₂×C₄²	1	36	yes	—
113	C₂²×C₃×C₈²	C₂²×C₈	1	64	yes	—
114	C₂²×C₃×C₈²	C₂²×C₈	1	144	yes	—
115	C₂²×C₃×C₈²	C₂³×C₄	1	12	yes	—
116	C₃×C₄²×C₁₆	C₄×C₈	1	288	yes	—
117	C₃×C₄²×C₁₆	C₂×C₄²	1	144	yes	—
118	C₃×C₄²×C₁₆	C₂²×C₈	1	288	yes	—
119	C₃×C₄²×C₁₆	C₂³×C₄	1	48	yes	—
120	C₂×C₃×C₈×C₁₆	C₄×C₈	1	1152	yes	—
121	C₂×C₃×C₈×C₁₆	C₂×C₁₆	1	4608	yes	direct product factor
122	C₂×C₃×C₈×C₁₆	C₂×C₄²	1	288	yes	—
123	C₂×C₃×C₈×C₁₆	C₂²×C₈	1	768	yes	—
124	C₂×C₃×C₈×C₁₆	C₂²×C₈	1	1152	yes	—
125	C₂×C₃×C₈×C₁₆	C₂³×C₄	1	96	yes	—
126	C₃×C₄×C₈²	C₄×C₈	1	144	yes	—
127	C₃×C₄×C₈²	C₂×C₄²	1	6	yes	—
128	C₃×C₄×C₈²	C₂×C₄²	1	36	yes	—
129	C₃×C₄×C₈²	C₂×C₄²	1	72	yes	—
130	C₃×C₄×C₈²	C₂²×C₈	1	144	yes	—
131	C₃×C₄×C₈²	C₂³×C₄	1	9	yes	—
132	C₃×C₄×C₈²	C₂³×C₄	1	12	yes	—
133	C₃×C₄×C₈²	C₂³×C₄	1	24	yes	—
134	C₃×C₄×C₈²	C₂⁵	1	1	yes	characteristic
135	C₃×C₁₆²	C₂²×C₈	1	1024	yes	direct product factor
136	C₂³×C₄×C₁₆	C₃×C₄²	1	24	yes	—
137	C₂³×C₄×C₁₆	C₂×C₃×C₈	1	48	yes	—
138	C₂²×C₄²×C₈	C₃×C₄²	1	4	yes	—
139	C₂²×C₄²×C₈	C₂²×C₃×C₄	1	3	yes	—
140	C₂³×C₈²	C₂×C₃×C₈	1	24	yes	—
141	C₂³×C₈²	C₂²×C₃×C₄	1	4	yes	—
142	C₂×C₄²×C₁₆	C₃×C₄²	1	72	yes	—
143	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	144	yes	—
144	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	72	yes	—
145	C₂²×C₈×C₁₆	C₃×C₁₆	1	768	yes	direct product factor
146	C₂²×C₈×C₁₆	C₃×C₄²	1	144	yes	—
147	C₂²×C₈×C₁₆	C₂×C₃×C₈	1	576	yes	—
148	C₂²×C₈×C₁₆	C₂×C₃×C₈	1	384	yes	—
149	C₂²×C₈×C₁₆	C₂²×C₃×C₄	1	144	yes	—
150	C₂×C₄×C₈²	C₃×C₄²	1	36	yes	—
151	C₂×C₄×C₈²	C₂×C₃×C₈	1	72	yes	—
152	C₂×C₄×C₈²	C₂²×C₃×C₄	1	9	yes	—
153	C₂×C₄×C₈²	C₂²×C₃×C₄	1	12	yes	—
154	C₂×C₄×C₈²	C₂²×C₃×C₄	1	36	yes	—
155	C₂×C₄×C₈²	C₂⁴×C₃	1	3	yes	—
156	C₄×C₈×C₁₆	C₃×C₄²	1	144	yes	—
157	C₄×C₈×C₁₆	C₂×C₃×C₈	1	576	yes	—
158	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	72	yes	—
159	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	144	yes	—
160	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	192	yes	—
161	C₄×C₈×C₁₆	C₂⁴×C₃	1	24	yes	—
162	C₂×C₁₆²	C₂×C₃×C₈	1	1536	yes	direct product factor
163	C₂×C₁₆²	C₂²×C₃×C₄	1	256	yes	—
164	C₈³	C₃×C₄²	1	24	yes	—
165	C₈³	C₂²×C₃×C₄	1	36	yes	—
166	C₈³	C₂⁴×C₃	1	4	yes	—
167	C₂⁴×C₃×C₈	C₈²	1	16	yes	—
168	C₂⁴×C₃×C₈	C₂×C₄×C₈	1	12	yes	—
169	C₂³×C₃×C₄²	C₄³	1	1	yes	characteristic
170	C₂³×C₃×C₄²	C₂×C₄×C₈	1	6	yes	—
171	C₂³×C₃×C₁₆	C₈²	1	384	yes	—
172	C₂³×C₃×C₁₆	C₄×C₁₆	1	768	yes	—
173	C₂³×C₃×C₁₆	C₂×C₄×C₈	1	288	yes	—
174	C₂²×C₃×C₄×C₈	C₈²	1	144	yes	—
175	C₂²×C₃×C₄×C₈	C₄×C₁₆	1	384	yes	—
176	C₂²×C₃×C₄×C₈	C₄³	1	18	yes	—
177	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	36	yes	—
178	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	36	yes	—
179	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	72	yes	—
180	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	96	yes	—
181	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	144	yes	—
182	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	192	yes	—
183	C₂²×C₃×C₄×C₈	C₂²×C₄²	1	18	yes	—
184	C₂²×C₃×C₄×C₈	C₂³×C₈	1	36	yes	—
185	C₂×C₃×C₄³	C₄³	1	3	yes	—
186	C₂×C₃×C₄³	C₂×C₄×C₈	1	18	yes	—
187	C₂×C₃×C₄³	C₂²×C₄²	1	3	yes	—
188	C₂×C₃×C₄×C₁₆	C₈²	1	1152	yes	—
189	C₂×C₃×C₄×C₁₆	C₄×C₁₆	1	2304	yes	—
190	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	288	yes	—
191	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	576	yes	—
192	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	1152	yes	—
193	C₂×C₃×C₄×C₁₆	C₂²×C₁₆	1	2304	yes	—
194	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	96	yes	—
195	C₂×C₃×C₄×C₁₆	C₂³×C₈	1	192	yes	—
196	C₃×C₄²×C₈	C₈²	1	96	yes	—
197	C₃×C₄²×C₈	C₄³	1	18	yes	—
198	C₃×C₄²×C₈	C₂×C₄×C₈	1	36	yes	—
199	C₃×C₄²×C₈	C₂×C₄×C₈	1	72	yes	—
200	C₃×C₄²×C₈	C₂×C₄×C₈	1	144	yes	—
201	C₃×C₄²×C₈	C₂²×C₄²	1	9	yes	—
202	C₃×C₄²×C₈	C₂²×C₄²	1	16	yes	—
203	C₃×C₄²×C₈	C₂²×C₄²	1	18	yes	—
204	C₃×C₄²×C₈	C₂³×C₈	1	36	yes	—
205	C₃×C₄²×C₈	C₂⁴×C₄	1	3	yes	—
206	C₂×C₃×C₈²	C₄×C₁₆	1	1152	yes	—
207	C₂×C₃×C₈²	C₄³	1	24	yes	—
208	C₂×C₃×C₈²	C₂×C₄×C₈	1	288	yes	—
209	C₂×C₃×C₈²	C₂×C₄×C₈	1	288	yes	—
210	C₂×C₃×C₈²	C₂²×C₁₆	1	1152	yes	—
211	C₂×C₃×C₈²	C₂²×C₄²	1	36	yes	—
212	C₂×C₃×C₈²	C₂³×C₈	1	96	yes	—
213	C₂×C₃×C₈²	C₂³×C₈	1	96	yes	—
214	C₂×C₃×C₈²	C₂⁴×C₄	1	4	yes	—
215	C₃×C₈×C₁₆	C₂×C₄×C₈	1	1152	yes	—
216	C₃×C₈×C₁₆	C₂²×C₁₆	1	3072	yes	direct product factor
217	C₃×C₈×C₁₆	C₂³×C₈	1	384	yes	—
218	C₂⁴×C₁₆	C₃×C₄×C₈	1	48	yes	—
219	C₂³×C₄×C₈	C₃×C₄×C₈	1	24	yes	—
220	C₂³×C₄×C₈	C₂×C₃×C₄²	1	6	yes	—
221	C₂³×C₄×C₈	C₂²×C₃×C₈	1	12	yes	—
222	C₂²×C₄³	C₂×C₃×C₄²	1	1	yes	characteristic
223	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	288	yes	—
224	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	384	yes	—
225	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	144	yes	—
226	C₂²×C₄×C₁₆	C₂×C₃×C₁₆	1	768	yes	—
227	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	144	yes	—
228	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	288	yes	—
229	C₂×C₄²×C₈	C₃×C₄×C₈	1	72	yes	—
230	C₂×C₄²×C₈	C₂×C₃×C₄²	1	9	yes	—
231	C₂×C₄²×C₈	C₂×C₃×C₄²	1	18	yes	—
232	C₂×C₄²×C₈	C₂×C₃×C₄²	1	24	yes	—
233	C₂×C₄²×C₈	C₂²×C₃×C₈	1	36	yes	—
234	C₂×C₄²×C₈	C₂³×C₃×C₄	1	9	yes	—
235	C₂²×C₈²	C₃×C₄×C₈	1	144	yes	—
236	C₂²×C₈²	C₂×C₃×C₁₆	1	384	yes	—
237	C₂²×C₈²	C₂×C₃×C₄²	1	36	yes	—
238	C₂²×C₈²	C₂²×C₃×C₈	1	64	yes	—
239	C₂²×C₈²	C₂²×C₃×C₈	1	144	yes	—
240	C₂²×C₈²	C₂³×C₃×C₄	1	12	yes	—
241	C₄²×C₁₆	C₃×C₄×C₈	1	288	yes	—
242	C₄²×C₁₆	C₂×C₃×C₄²	1	144	yes	—
243	C₄²×C₁₆	C₂²×C₃×C₈	1	288	yes	—
244	C₄²×C₁₆	C₂³×C₃×C₄	1	48	yes	—
245	C₂×C₈×C₁₆	C₃×C₄×C₈	1	1152	yes	—
246	C₂×C₈×C₁₆	C₂×C₃×C₁₆	1	4608	yes	direct product factor
247	C₂×C₈×C₁₆	C₂×C₃×C₄²	1	288	yes	—
248	C₂×C₈×C₁₆	C₂²×C₃×C₈	1	768	yes	—
249	C₂×C₈×C₁₆	C₂²×C₃×C₈	1	1152	yes	—
250	C₂×C₈×C₁₆	C₂³×C₃×C₄	1	96	yes	—
251	C₄×C₈²	C₃×C₄×C₈	1	144	yes	—
252	C₄×C₈²	C₂×C₃×C₄²	1	6	yes	—
253	C₄×C₈²	C₂×C₃×C₄²	1	36	yes	—
254	C₄×C₈²	C₂×C₃×C₄²	1	72	yes	—
255	C₄×C₈²	C₂²×C₃×C₈	1	144	yes	—
256	C₄×C₈²	C₂³×C₃×C₄	1	9	yes	—
257	C₄×C₈²	C₂³×C₃×C₄	1	12	yes	—
258	C₄×C₈²	C₂³×C₃×C₄	1	24	yes	—
259	C₄×C₈²	C₂⁵×C₃	1	1	yes	characteristic
260	C₁₆²	C₂²×C₃×C₈	1	1024	yes	direct product factor
261	C₂⁴×C₃×C₄	C₂×C₈²	1	4	yes	—
262	C₂⁴×C₃×C₄	C₄²×C₈	1	3	yes	—
263	C₂³×C₃×C₈	C₈×C₁₆	1	384	yes	—
264	C₂³×C₃×C₈	C₂×C₈²	1	96	yes	—
265	C₂³×C₃×C₈	C₂×C₈²	1	96	yes	—
266	C₂³×C₃×C₈	C₄²×C₈	1	36	yes	—
267	C₂³×C₃×C₈	C₂×C₄×C₁₆	1	192	yes	—
268	C₂³×C₃×C₈	C₂²×C₄×C₈	1	36	yes	—
269	C₂²×C₃×C₄²	C₂×C₈²	1	36	yes	—
270	C₂²×C₃×C₄²	C₄²×C₈	1	9	yes	—
271	C₂²×C₃×C₄²	C₄²×C₈	1	16	yes	—
272	C₂²×C₃×C₄²	C₄²×C₈	1	18	yes	—
273	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	96	yes	—
274	C₂²×C₃×C₄²	C₂×C₄³	1	3	yes	—
275	C₂²×C₃×C₄²	C₂²×C₄×C₈	1	18	yes	—
276	C₂²×C₃×C₁₆	C₈×C₁₆	1	3072	yes	direct product factor
277	C₂²×C₃×C₁₆	C₂×C₈²	1	1152	yes	—
278	C₂²×C₃×C₁₆	C₂×C₄×C₁₆	1	2304	yes	—
279	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	192	yes	—
280	C₂×C₃×C₄×C₈	C₈×C₁₆	1	1152	yes	—
281	C₂×C₃×C₄×C₈	C₂×C₈²	1	288	yes	—
282	C₂×C₃×C₄×C₈	C₂×C₈²	1	288	yes	—
283	C₂×C₃×C₄×C₈	C₄²×C₈	1	36	yes	—
284	C₂×C₃×C₄×C₈	C₄²×C₈	1	72	yes	—
285	C₂×C₃×C₄×C₈	C₄²×C₈	1	144	yes	—
286	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	288	yes	—
287	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	576	yes	—
288	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	1152	yes	—
289	C₂×C₃×C₄×C₈	C₂×C₄³	1	18	yes	—
290	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	36	yes	—
291	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	36	yes	—
292	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	72	yes	—
293	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	96	yes	—
294	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	144	yes	—
295	C₂×C₃×C₄×C₈	C₂³×C₁₆	1	288	yes	—
296	C₂×C₃×C₄×C₈	C₂³×C₄²	1	6	yes	—
297	C₂×C₃×C₄×C₈	C₂⁴×C₈	1	12	yes	—
298	C₃×C₄³	C₂×C₈²	1	24	yes	—
299	C₃×C₄³	C₄²×C₈	1	18	yes	—
300	C₃×C₄³	C₂×C₄³	1	3	yes	—
301	C₃×C₄³	C₂²×C₄×C₈	1	18	yes	—
302	C₃×C₄³	C₂³×C₄²	1	1	yes	characteristic
303	C₃×C₄×C₁₆	C₂×C₈²	1	1152	yes	—
304	C₃×C₄×C₁₆	C₂×C₄×C₁₆	1	2304	yes	—
305	C₃×C₄×C₁₆	C₂²×C₄×C₈	1	384	yes	—
306	C₃×C₄×C₁₆	C₂³×C₁₆	1	768	yes	—
307	C₃×C₈²	C₄²×C₈	1	96	yes	—
308	C₃×C₈²	C₂×C₄×C₁₆	1	1152	yes	—
309	C₃×C₈²	C₂²×C₄×C₈	1	144	yes	—
310	C₃×C₈²	C₂³×C₁₆	1	384	yes	—
311	C₃×C₈²	C₂⁴×C₈	1	16	yes	—
312	C₂⁴×C₈	C₃×C₈²	1	16	yes	—
313	C₂⁴×C₈	C₂×C₃×C₄×C₈	1	12	yes	—
314	C₂³×C₄²	C₃×C₄³	1	1	yes	characteristic
315	C₂³×C₄²	C₂×C₃×C₄×C₈	1	6	yes	—
316	C₂³×C₁₆	C₃×C₈²	1	384	yes	—
317	C₂³×C₁₆	C₃×C₄×C₁₆	1	768	yes	—
318	C₂³×C₁₆	C₂×C₃×C₄×C₈	1	288	yes	—
319	C₂²×C₄×C₈	C₃×C₈²	1	144	yes	—
320	C₂²×C₄×C₈	C₃×C₄×C₁₆	1	384	yes	—
321	C₂²×C₄×C₈	C₃×C₄³	1	18	yes	—
322	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	36	yes	—
323	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	36	yes	—
324	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	72	yes	—
325	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	96	yes	—
326	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	144	yes	—
327	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	192	yes	—
328	C₂²×C₄×C₈	C₂²×C₃×C₄²	1	18	yes	—
329	C₂²×C₄×C₈	C₂³×C₃×C₈	1	36	yes	—
330	C₂×C₄³	C₃×C₄³	1	3	yes	—
331	C₂×C₄³	C₂×C₃×C₄×C₈	1	18	yes	—
332	C₂×C₄³	C₂²×C₃×C₄²	1	3	yes	—
333	C₂×C₄×C₁₆	C₃×C₈²	1	1152	yes	—
334	C₂×C₄×C₁₆	C₃×C₄×C₁₆	1	2304	yes	—
335	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	288	yes	—
336	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	576	yes	—
337	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	1152	yes	—
338	C₂×C₄×C₁₆	C₂²×C₃×C₁₆	1	2304	yes	—
339	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	96	yes	—
340	C₂×C₄×C₁₆	C₂³×C₃×C₈	1	192	yes	—
341	C₄²×C₈	C₃×C₈²	1	96	yes	—
342	C₄²×C₈	C₃×C₄³	1	18	yes	—
343	C₄²×C₈	C₂×C₃×C₄×C₈	1	36	yes	—
344	C₄²×C₈	C₂×C₃×C₄×C₈	1	72	yes	—
345	C₄²×C₈	C₂×C₃×C₄×C₈	1	144	yes	—
346	C₄²×C₈	C₂²×C₃×C₄²	1	9	yes	—
347	C₄²×C₈	C₂²×C₃×C₄²	1	16	yes	—
348	C₄²×C₈	C₂²×C₃×C₄²	1	18	yes	—
349	C₄²×C₈	C₂³×C₃×C₈	1	36	yes	—
350	C₄²×C₈	C₂⁴×C₃×C₄	1	3	yes	—
351	C₂×C₈²	C₃×C₄×C₁₆	1	1152	yes	—
352	C₂×C₈²	C₃×C₄³	1	24	yes	—
353	C₂×C₈²	C₂×C₃×C₄×C₈	1	288	yes	—
354	C₂×C₈²	C₂×C₃×C₄×C₈	1	288	yes	—
355	C₂×C₈²	C₂²×C₃×C₁₆	1	1152	yes	—
356	C₂×C₈²	C₂²×C₃×C₄²	1	36	yes	—
357	C₂×C₈²	C₂³×C₃×C₈	1	96	yes	—
358	C₂×C₈²	C₂³×C₃×C₈	1	96	yes	—
359	C₂×C₈²	C₂⁴×C₃×C₄	1	4	yes	—
360	C₈×C₁₆	C₂×C₃×C₄×C₈	1	1152	yes	—
361	C₈×C₁₆	C₂²×C₃×C₁₆	1	3072	yes	direct product factor
362	C₈×C₁₆	C₂³×C₃×C₈	1	384	yes	—
363	C₂⁵×C₃	C₄×C₈²	1	1	yes	characteristic
364	C₂³×C₃×C₄	C₄×C₈²	1	9	yes	—
365	C₂³×C₃×C₄	C₄×C₈²	1	12	yes	—
366	C₂³×C₃×C₄	C₄×C₈²	1	24	yes	—
367	C₂³×C₃×C₄	C₂×C₈×C₁₆	1	96	yes	—
368	C₂³×C₃×C₄	C₄²×C₁₆	1	48	yes	—
369	C₂³×C₃×C₄	C₂²×C₈²	1	12	yes	—
370	C₂³×C₃×C₄	C₂×C₄²×C₈	1	9	yes	—
371	C₂²×C₃×C₈	C₁₆²	1	1024	yes	direct product factor
372	C₂²×C₃×C₈	C₄×C₈²	1	144	yes	—
373	C₂²×C₃×C₈	C₂×C₈×C₁₆	1	768	yes	—
374	C₂²×C₃×C₈	C₂×C₈×C₁₆	1	1152	yes	—
375	C₂²×C₃×C₈	C₄²×C₁₆	1	288	yes	—
376	C₂²×C₃×C₈	C₂²×C₈²	1	64	yes	—
377	C₂²×C₃×C₈	C₂²×C₈²	1	144	yes	—
378	C₂²×C₃×C₈	C₂×C₄²×C₈	1	36	yes	—
379	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	288	yes	—
380	C₂²×C₃×C₈	C₂³×C₄×C₈	1	12	yes	—
381	C₂×C₃×C₄²	C₄×C₈²	1	6	yes	—
382	C₂×C₃×C₄²	C₄×C₈²	1	36	yes	—
383	C₂×C₃×C₄²	C₄×C₈²	1	72	yes	—
384	C₂×C₃×C₄²	C₂×C₈×C₁₆	1	288	yes	—
385	C₂×C₃×C₄²	C₄²×C₁₆	1	144	yes	—
386	C₂×C₃×C₄²	C₂²×C₈²	1	36	yes	—
387	C₂×C₃×C₄²	C₂×C₄²×C₈	1	9	yes	—
388	C₂×C₃×C₄²	C₂×C₄²×C₈	1	18	yes	—
389	C₂×C₃×C₄²	C₂×C₄²×C₈	1	24	yes	—
390	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	144	yes	—
391	C₂×C₃×C₄²	C₂²×C₄³	1	1	yes	characteristic
392	C₂×C₃×C₄²	C₂³×C₄×C₈	1	6	yes	—
393	C₂×C₃×C₁₆	C₂×C₈×C₁₆	1	4608	yes	direct product factor
394	C₂×C₃×C₁₆	C₂²×C₈²	1	384	yes	—
395	C₂×C₃×C₁₆	C₂²×C₄×C₁₆	1	768	yes	—
396	C₃×C₄×C₈	C₄×C₈²	1	144	yes	—
397	C₃×C₄×C₈	C₂×C₈×C₁₆	1	1152	yes	—
398	C₃×C₄×C₈	C₄²×C₁₆	1	288	yes	—
399	C₃×C₄×C₈	C₂²×C₈²	1	144	yes	—
400	C₃×C₄×C₈	C₂×C₄²×C₈	1	72	yes	—
401	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	288	yes	—
402	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	384	yes	—
403	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	144	yes	—
404	C₃×C₄×C₈	C₂³×C₄×C₈	1	24	yes	—
405	C₃×C₄×C₈	C₂⁴×C₁₆	1	48	yes	—
406	C₂⁴×C₄	C₂×C₃×C₈²	1	4	yes	—
407	C₂⁴×C₄	C₃×C₄²×C₈	1	3	yes	—
408	C₂³×C₈	C₃×C₈×C₁₆	1	384	yes	—
409	C₂³×C₈	C₂×C₃×C₈²	1	96	yes	—
410	C₂³×C₈	C₂×C₃×C₈²	1	96	yes	—
411	C₂³×C₈	C₃×C₄²×C₈	1	36	yes	—
412	C₂³×C₈	C₂×C₃×C₄×C₁₆	1	192	yes	—
413	C₂³×C₈	C₂²×C₃×C₄×C₈	1	36	yes	—
414	C₂²×C₄²	C₂×C₃×C₈²	1	36	yes	—
415	C₂²×C₄²	C₃×C₄²×C₈	1	9	yes	—
416	C₂²×C₄²	C₃×C₄²×C₈	1	16	yes	—
417	C₂²×C₄²	C₃×C₄²×C₈	1	18	yes	—
418	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	96	yes	—
419	C₂²×C₄²	C₂×C₃×C₄³	1	3	yes	—
420	C₂²×C₄²	C₂²×C₃×C₄×C₈	1	18	yes	—
421	C₂²×C₁₆	C₃×C₈×C₁₆	1	3072	yes	direct product factor
422	C₂²×C₁₆	C₂×C₃×C₈²	1	1152	yes	—
423	C₂²×C₁₆	C₂×C₃×C₄×C₁₆	1	2304	yes	—
424	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	192	yes	—
425	C₂×C₄×C₈	C₃×C₈×C₁₆	1	1152	yes	—
426	C₂×C₄×C₈	C₂×C₃×C₈²	1	288	yes	—
427	C₂×C₄×C₈	C₂×C₃×C₈²	1	288	yes	—
428	C₂×C₄×C₈	C₃×C₄²×C₈	1	36	yes	—
429	C₂×C₄×C₈	C₃×C₄²×C₈	1	72	yes	—
430	C₂×C₄×C₈	C₃×C₄²×C₈	1	144	yes	—
431	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	288	yes	—
432	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	576	yes	—
433	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	1152	yes	—
434	C₂×C₄×C₈	C₂×C₃×C₄³	1	18	yes	—
435	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	36	yes	—
436	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	36	yes	—
437	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	72	yes	—
438	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	96	yes	—
439	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	144	yes	—
440	C₂×C₄×C₈	C₂³×C₃×C₁₆	1	288	yes	—
441	C₂×C₄×C₈	C₂³×C₃×C₄²	1	6	yes	—
442	C₂×C₄×C₈	C₂⁴×C₃×C₈	1	12	yes	—
443	C₄³	C₂×C₃×C₈²	1	24	yes	—
444	C₄³	C₃×C₄²×C₈	1	18	yes	—
445	C₄³	C₂×C₃×C₄³	1	3	yes	—
446	C₄³	C₂²×C₃×C₄×C₈	1	18	yes	—
447	C₄³	C₂³×C₃×C₄²	1	1	yes	characteristic
448	C₄×C₁₆	C₂×C₃×C₈²	1	1152	yes	—
449	C₄×C₁₆	C₂×C₃×C₄×C₁₆	1	2304	yes	—
450	C₄×C₁₆	C₂²×C₃×C₄×C₈	1	384	yes	—
451	C₄×C₁₆	C₂³×C₃×C₁₆	1	768	yes	—
452	C₈²	C₃×C₄²×C₈	1	96	yes	—
453	C₈²	C₂×C₃×C₄×C₁₆	1	1152	yes	—
454	C₈²	C₂²×C₃×C₄×C₈	1	144	yes	—
455	C₈²	C₂³×C₃×C₁₆	1	384	yes	—
456	C₈²	C₂⁴×C₃×C₈	1	16	yes	—
457	C₂⁴×C₃	C₈³	1	4	yes	—
458	C₂⁴×C₃	C₄×C₈×C₁₆	1	24	yes	—
459	C₂⁴×C₃	C₂×C₄×C₈²	1	3	yes	—
460	C₂²×C₃×C₄	C₈³	1	36	yes	—
461	C₂²×C₃×C₄	C₂×C₁₆²	1	256	yes	—
462	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	72	yes	—
463	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	144	yes	—
464	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	192	yes	—
465	C₂²×C₃×C₄	C₂×C₄×C₈²	1	9	yes	—
466	C₂²×C₃×C₄	C₂×C₄×C₈²	1	12	yes	—
467	C₂²×C₃×C₄	C₂×C₄×C₈²	1	36	yes	—
468	C₂²×C₃×C₄	C₂²×C₈×C₁₆	1	144	yes	—
469	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	72	yes	—
470	C₂²×C₃×C₄	C₂³×C₈²	1	4	yes	—
471	C₂²×C₃×C₄	C₂²×C₄²×C₈	1	3	yes	—
472	C₂×C₃×C₈	C₂×C₁₆²	1	1536	yes	direct product factor
473	C₂×C₃×C₈	C₄×C₈×C₁₆	1	576	yes	—
474	C₂×C₃×C₈	C₂×C₄×C₈²	1	72	yes	—
475	C₂×C₃×C₈	C₂²×C₈×C₁₆	1	576	yes	—
476	C₂×C₃×C₈	C₂²×C₈×C₁₆	1	384	yes	—
477	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	144	yes	—
478	C₂×C₃×C₈	C₂³×C₈²	1	24	yes	—
479	C₂×C₃×C₈	C₂³×C₄×C₁₆	1	48	yes	—
480	C₃×C₄²	C₈³	1	24	yes	—
481	C₃×C₄²	C₄×C₈×C₁₆	1	144	yes	—
482	C₃×C₄²	C₂×C₄×C₈²	1	36	yes	—
483	C₃×C₄²	C₂²×C₈×C₁₆	1	144	yes	—
484	C₃×C₄²	C₂×C₄²×C₁₆	1	72	yes	—
485	C₃×C₄²	C₂²×C₄²×C₈	1	4	yes	—
486	C₃×C₄²	C₂³×C₄×C₁₆	1	24	yes	—
487	C₃×C₁₆	C₂²×C₈×C₁₆	1	768	yes	direct product factor
488	C₂⁵	C₃×C₄×C₈²	1	1	yes	characteristic
489	C₂³×C₄	C₃×C₄×C₈²	1	9	yes	—
490	C₂³×C₄	C₃×C₄×C₈²	1	12	yes	—
491	C₂³×C₄	C₃×C₄×C₈²	1	24	yes	—
492	C₂³×C₄	C₂×C₃×C₈×C₁₆	1	96	yes	—
493	C₂³×C₄	C₃×C₄²×C₁₆	1	48	yes	—
494	C₂³×C₄	C₂²×C₃×C₈²	1	12	yes	—
495	C₂³×C₄	C₂×C₃×C₄²×C₈	1	9	yes	—
496	C₂²×C₈	C₃×C₁₆²	1	1024	yes	direct product factor
497	C₂²×C₈	C₃×C₄×C₈²	1	144	yes	—
498	C₂²×C₈	C₂×C₃×C₈×C₁₆	1	768	yes	—
499	C₂²×C₈	C₂×C₃×C₈×C₁₆	1	1152	yes	—
500	C₂²×C₈	C₃×C₄²×C₁₆	1	288	yes	—
501	C₂²×C₈	C₂²×C₃×C₈²	1	64	yes	—
502	C₂²×C₈	C₂²×C₃×C₈²	1	144	yes	—
503	C₂²×C₈	C₂×C₃×C₄²×C₈	1	36	yes	—
504	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	288	yes	—
505	C₂²×C₈	C₂³×C₃×C₄×C₈	1	12	yes	—
506	C₂×C₄²	C₃×C₄×C₈²	1	6	yes	—
507	C₂×C₄²	C₃×C₄×C₈²	1	36	yes	—
508	C₂×C₄²	C₃×C₄×C₈²	1	72	yes	—
509	C₂×C₄²	C₂×C₃×C₈×C₁₆	1	288	yes	—
510	C₂×C₄²	C₃×C₄²×C₁₆	1	144	yes	—
511	C₂×C₄²	C₂²×C₃×C₈²	1	36	yes	—
512	C₂×C₄²	C₂×C₃×C₄²×C₈	1	9	yes	—
513	C₂×C₄²	C₂×C₃×C₄²×C₈	1	18	yes	—
514	C₂×C₄²	C₂×C₃×C₄²×C₈	1	24	yes	—
515	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	144	yes	—
516	C₂×C₄²	C₂²×C₃×C₄³	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₃×C₄×C₈	1	6	yes	—
518	C₂×C₁₆	C₂×C₃×C₈×C₁₆	1	4608	yes	direct product factor
519	C₂×C₁₆	C₂²×C₃×C₈²	1	384	yes	—
520	C₂×C₁₆	C₂²×C₃×C₄×C₁₆	1	768	yes	—
521	C₄×C₈	C₃×C₄×C₈²	1	144	yes	—
522	C₄×C₈	C₂×C₃×C₈×C₁₆	1	1152	yes	—
523	C₄×C₈	C₃×C₄²×C₁₆	1	288	yes	—
524	C₄×C₈	C₂²×C₃×C₈²	1	144	yes	—
525	C₄×C₈	C₂×C₃×C₄²×C₈	1	72	yes	—
526	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	288	yes	—
527	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	384	yes	—
528	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	144	yes	—
529	C₄×C₈	C₂³×C₃×C₄×C₈	1	24	yes	—
530	C₄×C₈	C₂⁴×C₃×C₁₆	1	48	yes	—
531	C₂³×C₃	C₄×C₁₆²	1	64	yes	—
532	C₂³×C₃	C₈²×C₁₆	1	48	yes	—
533	C₂³×C₃	C₂×C₄×C₈×C₁₆	1	36	yes	—
534	C₂³×C₃	C₂×C₈³	1	6	yes	—
535	C₂³×C₃	C₂²×C₄×C₈²	1	1	yes	characteristic
536	C₂×C₃×C₄	C₄×C₁₆²	1	192	yes	—
537	C₂×C₃×C₄	C₂²×C₁₆²	1	192	yes	—
538	C₂×C₃×C₄	C₈²×C₁₆	1	144	yes	—
539	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	36	yes	—
540	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	72	yes	—
541	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	144	yes	—
542	C₂×C₃×C₄	C₂³×C₈×C₁₆	1	24	yes	—
543	C₂×C₃×C₄	C₂²×C₄²×C₁₆	1	12	yes	—
544	C₂×C₃×C₄	C₂×C₈³	1	18	yes	—
545	C₂×C₃×C₄	C₂²×C₄×C₈²	1	6	yes	—
546	C₃×C₈	C₂²×C₁₆²	1	256	yes	direct product factor
547	C₃×C₈	C₂×C₄×C₈×C₁₆	1	144	yes	—
548	C₃×C₈	C₂³×C₈×C₁₆	1	48	yes	—
549	C₂⁴	C₃×C₄×C₈×C₁₆	1	24	yes	—
550	C₂⁴	C₃×C₈³	1	4	yes	—
551	C₂⁴	C₂×C₃×C₄×C₈²	1	3	yes	—
552	C₂²×C₄	C₂×C₃×C₁₆²	1	256	yes	—
553	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	72	yes	—
554	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	144	yes	—
555	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	192	yes	—
556	C₂²×C₄	C₂²×C₃×C₈×C₁₆	1	144	yes	—
557	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	72	yes	—
558	C₂²×C₄	C₃×C₈³	1	36	yes	—
559	C₂²×C₄	C₂×C₃×C₄×C₈²	1	9	yes	—
560	C₂²×C₄	C₂×C₃×C₄×C₈²	1	12	yes	—
561	C₂²×C₄	C₂×C₃×C₄×C₈²	1	36	yes	—
562	C₂²×C₄	C₂³×C₃×C₈²	1	4	yes	—
563	C₂²×C₄	C₂²×C₃×C₄²×C₈	1	3	yes	—
564	C₂×C₈	C₂×C₃×C₁₆²	1	1536	yes	direct product factor
565	C₂×C₈	C₃×C₄×C₈×C₁₆	1	576	yes	—
566	C₂×C₈	C₂²×C₃×C₈×C₁₆	1	576	yes	—
567	C₂×C₈	C₂²×C₃×C₈×C₁₆	1	384	yes	—
568	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	144	yes	—
569	C₂×C₈	C₂³×C₃×C₄×C₁₆	1	48	yes	—
570	C₂×C₈	C₂×C₃×C₄×C₈²	1	72	yes	—
571	C₂×C₈	C₂³×C₃×C₈²	1	24	yes	—
572	C₄²	C₃×C₄×C₈×C₁₆	1	144	yes	—
573	C₄²	C₂²×C₃×C₈×C₁₆	1	144	yes	—
574	C₄²	C₂×C₃×C₄²×C₁₆	1	72	yes	—
575	C₄²	C₂³×C₃×C₄×C₁₆	1	24	yes	—
576	C₄²	C₃×C₈³	1	24	yes	—
577	C₄²	C₂×C₃×C₄×C₈²	1	36	yes	—
578	C₄²	C₂²×C₃×C₄²×C₈	1	4	yes	—
579	C₁₆	C₂²×C₃×C₈×C₁₆	1	768	yes	direct product factor
580	C₂²×C₃	C₈×C₁₆²	1	64	yes	direct product factor
581	C₂²×C₃	C₂×C₄×C₁₆²	1	48	yes	—
582	C₂²×C₃	C₂×C₈²×C₁₆	1	36	yes	—
583	C₂²×C₃	C₂²×C₄×C₈×C₁₆	1	6	yes	—
584	C₂²×C₃	C₂²×C₈³	1	1	yes	characteristic
585	C₃×C₄	C₂³×C₁₆²	1	16	yes	—
586	C₃×C₄	C₂×C₄×C₁₆²	1	48	yes	—
587	C₃×C₄	C₂×C₈²×C₁₆	1	36	yes	—
588	C₃×C₄	C₂²×C₄×C₈×C₁₆	1	12	yes	—
589	C₂³	C₃×C₄×C₁₆²	1	64	yes	—
590	C₂³	C₃×C₈²×C₁₆	1	48	yes	—
591	C₂³	C₂×C₃×C₄×C₈×C₁₆	1	36	yes	—
592	C₂³	C₂×C₃×C₈³	1	6	yes	—
593	C₂³	C₂²×C₃×C₄×C₈²	1	1	yes	characteristic
594	C₂×C₄	C₃×C₄×C₁₆²	1	192	yes	—
595	C₂×C₄	C₂²×C₃×C₁₆²	1	192	yes	—
596	C₂×C₄	C₃×C₈²×C₁₆	1	144	yes	—
597	C₂×C₄	C₂³×C₃×C₈×C₁₆	1	24	yes	—
598	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	36	yes	—
599	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	72	yes	—
600	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	144	yes	—
601	C₂×C₄	C₂²×C₃×C₄²×C₁₆	1	12	yes	—
602	C₂×C₄	C₂×C₃×C₈³	1	18	yes	—
603	C₂×C₄	C₂²×C₃×C₄×C₈²	1	6	yes	—
604	C₈	C₂²×C₃×C₁₆²	1	256	yes	direct product factor
605	C₈	C₂³×C₃×C₈×C₁₆	1	48	yes	—
606	C₈	C₂×C₃×C₄×C₈×C₁₆	1	144	yes	—
607	C₂×C₃	C₂×C₈×C₁₆²	1	24	yes	direct product factor
608	C₂×C₃	C₂²×C₄×C₁₆²	1	4	yes	—
609	C₂×C₃	C₂²×C₈²×C₁₆	1	3	yes	—
610	C₂²	C₃×C₈×C₁₆²	1	64	yes	direct product factor
611	C₂²	C₂×C₃×C₄×C₁₆²	1	48	yes	—
612	C₂²	C₂×C₃×C₈²×C₁₆	1	36	yes	—
613	C₂²	C₂²×C₃×C₄×C₈×C₁₆	1	6	yes	—
614	C₂²	C₂²×C₃×C₈³	1	1	yes	characteristic
615	C₄	C₂×C₃×C₄×C₁₆²	1	48	yes	—
616	C₄	C₂³×C₃×C₁₆²	1	16	yes	—
617	C₄	C₂×C₃×C₈²×C₁₆	1	36	yes	—
618	C₄	C₂²×C₃×C₄×C₈×C₁₆	1	12	yes	—
619	C₃	C₂²×C₈×C₁₆²	1	1	yes	characteristic, direct product factor, Sylow
620	C₂	C₂×C₃×C₈×C₁₆²	1	24	yes	direct product factor
621	C₂	C₂²×C₃×C₄×C₁₆²	1	4	yes	—
622	C₂	C₂²×C₃×C₈²×C₁₆	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈²	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₄×C₈²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₃×C₈×C₁₆²	C₂	direct (N × H)
4. C₂²×C₈×C₁₆²	C₃	direct (N × H)
13. C₃×C₈×C₁₆²	C₂²	direct (N × H)
16. C₂×C₈×C₁₆²	C₂×C₃	direct (N × H)
31. C₂²×C₃×C₁₆²	C₈	direct (N × H)
43. C₈×C₁₆²	C₂²×C₃	direct (N × H)
62. C₂²×C₃×C₈×C₁₆	C₁₆	direct (N × H)
73. C₂×C₃×C₁₆²	C₂×C₈	direct (N × H)
89. C₂²×C₁₆²	C₃×C₈	direct (N × H)
121. C₂×C₃×C₈×C₁₆	C₂×C₁₆	direct (N × H)
135. C₃×C₁₆²	C₂²×C₈	direct (N × H)
145. C₂²×C₈×C₁₆	C₃×C₁₆	direct (N × H)
162. C₂×C₁₆²	C₂×C₃×C₈	direct (N × H)
216. C₃×C₈×C₁₆	C₂²×C₁₆	direct (N × H)
246. C₂×C₈×C₁₆	C₂×C₃×C₁₆	direct (N × H)
260. C₁₆²	C₂²×C₃×C₈	direct (N × H)
276. C₂²×C₃×C₁₆	C₈×C₁₆	direct (N × H)
361. C₈×C₁₆	C₂²×C₃×C₁₆	direct (N × H)
371. C₂²×C₃×C₈	C₁₆²	direct (N × H)
393. C₂×C₃×C₁₆	C₂×C₈×C₁₆	direct (N × H)
421. C₂²×C₁₆	C₃×C₈×C₁₆	direct (N × H)
472. C₂×C₃×C₈	C₂×C₁₆²	direct (N × H)
487. C₃×C₁₆	C₂²×C₈×C₁₆	direct (N × H)
496. C₂²×C₈	C₃×C₁₆²	direct (N × H)
518. C₂×C₁₆	C₂×C₃×C₈×C₁₆	direct (N × H)
546. C₃×C₈	C₂²×C₁₆²	direct (N × H)
564. C₂×C₈	C₂×C₃×C₁₆²	direct (N × H)
579. C₁₆	C₂²×C₃×C₈×C₁₆	direct (N × H)
580. C₂²×C₃	C₈×C₁₆²	direct (N × H)
604. C₈	C₂²×C₃×C₁₆²	direct (N × H)
607. C₂×C₃	C₂×C₈×C₁₆²	direct (N × H)
610. C₂²	C₃×C₈×C₁₆²	direct (N × H)
619. C₃	C₂²×C₈×C₁₆²	direct (N × H)
620. C₂	C₂×C₃×C₈×C₁₆²	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₈²×C₁₆	2
C₂²×C₃×C₄×C₁₆²	2
C₂×C₃×C₈×C₁₆²	2
C₂²×C₈×C₁₆²	3

Subgroups — C22×C3×C8×C162 #72201876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₈×C₁₆² #72201876